All over the news I read that the yield curve is inverting.
I thought they were talking about the US Treasury Bond yield curve.
This seems to be the case when I read this article.

However there are still some things I don't grasp.

1) How does the yield change?

For me the US are emitting the bonds. For instance they may decide to try selling bonds with a maturity of 30 year and a yield of 2%. If I buy it, then I can resell it on the secondary market. If I do that, I am still selling a bond with a yield of 2%, so how can the yield of 30 year bond become lower if the US does not decide to emit a bond with a lower yield?

2) Are we considering the yield curve of the US Treasury bond?

When I asked question 1) to my colleague today, he told me that in fact, the yield curve people were talking about was the one of the inter-bank rate (like the LIBOR). This added confusion for me. Is it true? Is it how the yield change?

From this answer, it seems like we are talking about Zero coupon yield curve constructed via the bootstapping method. Is it true?

3) Is there other also yield curves from other countries to consider?

What if the US Treasury bond yield curve invert but not the German bond curve? Is it possible?

4) Where can I find informations about the current yield curve?

Is there an official site posting this curve somewhere?

5) Why do people believe yield curve inversion implies an upcoming recession? Is it a fallacy or is it sure?

When reading the news I kind of have the feeling that people are saying "Last two time yield curve inverted we had a recession", but it sounds not very logical to me. From a statistical point of view the number of occurence is not enough to reach any conclusion. Is there more serious reasons to believe that a recession will come when the yield curve invert?

so how can the yield of 30 year bond become lower if the US does not decide to emit a bond with a lower yield?

You're confusing yield with interest rate. If you buy a $100 1-year bond that pays 2% interest, you get $102 in one year. What if you paid $102 for that bond? Then you made no profit and your yield is zero.

So A lower yield indicates that investors are paying higher prices for those bonds. Typically investors want higher yields from (pay lower prices for) longer-term bonds since their money is locked up for a longer period (if they hold the bond to maturity, which most do not). An inverted curve indicates a lack of demand (lower prices, higher yields) in shorter-term bonds, possibly because of fears about the near-term economic future, or because longer-term bonds do better when interest rates fall.

Are we considering the yield curve of the US Treasury bond?

It depends on what you're talking about? each government (and LIBOR) has its own "yield curve" that is created from the rates/prices of the bonds it issues. (Bootstrapping is one of many methods to do this). So when someone says "the yield curve is inverting", the first question is: Which yield curve?

What if the US Treasury bond yield curve invert but not the German bond curve? Is it possible?

Why do people believe yield curve inversion implies an upcoming recession? Is it a fallacy or is it sure?

It's neither a fallacy nor certain. An inverting yield curve has preceded each of the past 7 recessions, dating back to 1970 (note that the yield curve was also inverted in 1966, but a recession did not occur until 1970), so it's reasonable to assume that another recession is possible. but not a certainty. It also does not mean that a recession has started. Over that time, a recession started on average 14 months after the curve inverted.

An average 14 months after the curve inverted kind of makes you think it's a self-fulfilling prophecy. That's plenty of time for people to stop investing because they believe a recession is coming, then voila! recession!
– Nathan LAug 29 at 14:27

Do note that a recession doesn't necessarily have anything to do with the stock market either. If people stopped investing and just spent the money (instead of saving it) you would have strong GDP growth despite a stock market crash.... The problem is that that doesn't happen. People are saving because they're worried about a recession and thereby are causing a recession.
– xyiousSep 2 at 16:42

As D Stanley put it, this is the difference between yield and interest rate. The bond might still be for $1000 at 2% interest rate (a $20 coupon), but it's being sold for a different price than $1000, due to a variety of factors.

One big factor is the present interest rate. If now those bonds are being issued at 1.5%, you can expect the old $20 coupon bonds to be sold at a premium. If current rates are 2.5%, they'd need to be sold at a discount.

Yield is how much you're getting in return divided by how much you're paying. It's ultimately set by the market.

2) Are we considering the yield curve of the US Treasury bond?

In US news, yes, people usually talk about the curve between longer term and shorter term US Treasury bonds.

But that's a good point: There is no single yield curve, and no single way for it to be "inverted". You could use different definitions of long and short term even within the US Treasury bond market.

3) Is there other also yield curves from other countries to consider?

Sure. Yield inversion needs some key ingredients, but any reliable country's government bonds (or similar financial instrument) could experience it, and that would be interesting information with particular implications in each case.

5) Why do people believe yield curve inversion implies an upcoming recession? Is it a fallacy or is it sure?

The longer term bonds (10, or 30 years) should naturally have a higher yield (meaning a lower price) than otherwise similar shorter bonds (3 months, or 2 years for example). That's because everything else being the same, investors should prefer being paid sooner rather than later.

The exception to this is when there's an expectation that future yields will be lower, so buying now helps you "lock in" the rates for a long time, or increase the premium when selling them.

Why would yields be lower? Well, it could be that there will be a lot of people selling out of other investments (like stocks) and will take a safe low return rather than keep money idle. It could also be that the Federal Reserve will be lowering new bond rates to stimulate the economy. These things are associated with economic recessions.

So does an inverted yield curve imply a recession? No, but it tells you that institutional investors and high net worth individuals (who own the vast majority of the stock and bond markets) think that it's likely enough to start preparing for it. And the amounts of money are large enough to move prices away from equilibrium in the most traded financial instrument in the world, the US Treasury bond.

They might be overreacting, or they might be insightful enough to see it coming. They might even be doing a self-fulfilling prophecy by scaring everyone about it. It's a sign that big money thinks a recession might be coming, but the real evidence is in the economy.